Just a little persopnal background for understanding, Ihor. Once more, I am
most definitely not knocking the use of good software, but neither do I accept
anything out of hand without question.

I didn't see coordinates until 'analytic geometry" in my graduation year [and it
was a year, not a semester]. The introduction soon led into the graphing and
analytic solution of relations and equations ...the conic sections. It all led
smoothly one into the other for ocmplete ocurse of study. As a teacher, I've
seen many changes. During those changing times I saw a speculative approach [in
the midst of several other trials] to teaching called "The spiral approach to
learning." The theory was that if students were exposed to a little more each
year, their knowledge would build as they come back to the topic on the spiral
in the next year, and the next. It didn't work.

Now, I see the same approach in a different colour, but still the same: Why not
teach the first few pages to the young. No depth of study, but just an
introduction ...and let's make it fun. Again, it will not work, and for the
same reasons, one of which is practice and retention. It's like picking up a
book and putting it down, picking it up later, and putting it down .... It's
far more absorbing to read the book continuously, so far as time allows, to keep
track of all the characters and twists and turns, and the reader gets thus more
out of it, and more readily.

In any event, I wish all well, and hope that there is some way to measure the
success with such devices vs those who study without them. It is so difficult
to compare apples and apples.

P.S. You say, "Math is not easy. Most kids don't learn it very well." I'd add
that math is fun, pure and simple, and the joy of it is expressed in the joy and
knowledge of the teacher in presenting it. I'd prefer one bar of Chopin to a
whole passage of fluff, and they have to first practice their scales. Scales are
not fun. They are absolutely necessary.

This material is based upon work supported by the
National Science Foundation under Grant DUE-0226284.
Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the author(s)
and do not necessarily reflect the views of the
National Science Foundation.